Econ 100A-Spring 2007
Problem Set 5 Answers
Department of Economics
University of California, Berkeley
PROBLEM SET 5 ANSWER SHEET
TRUE or FALSE
For each statement below, decide whether it is true or false and provide
assumptions you find necessary to come to that conclusion.
In a Bertrand duopoly with a homogeneous good, an increase one firm’s marginal cost will
result in an increase in both firms’ equilibrium prices.
[Could be true or false.
case where the two firms have different costs, and assume they both have constant marginal
Then the Bertrand equilibrium has price equal to (or slightly below) the
marginal cost of the high-cost firm. If the cost increase occurs for the high-cost firm, then
equilibrium price will increase.
If it occurs for the low-cost firm, there will be no effect on
equilibrium price (as long as the increase is not so large as to turn the low-cost firm into the
If duopolists’ products are differentiated, the statement will be True.
case, Firms that compete a la Bertrand have reaction functions that are increasing.
words, when a rival raises its price, a firm will react by raising its price as well.
Now, a rise
in a firm’s marginal cost will naturally result in it charging a higher price, i.e., shifts out its
Since its rival’s reaction is increasing, the new equilibrium will have both
If each new breakfast cereal brand must pay a fixed “slotting allowance” to get space on the
shelves of grocery stores, then the number of brands in a monopolistically competitive
industry will fall, and the market share of the surviving brands will increase.
[This can be
true if the monopolistically competitive industry is in long run equilibrium, i.e., firms freely
enter and exit in response to profit.
After the increase in the fee, which amounts to an
increase in fixed cost, firms no longer break even as the original equilibrium price.
that was the only price that had firms break even at the lower cost, the corresponding
number of firms is not sustainable.
The number of firms must fall in order to be profitable at
the higher cost, and hence, the number of brands must fall since there is one brand per firm
in the monopolistic competition model.
Since another feature of that model is that brands
are treated symmetrically by consumers, the market share of each firm in the new
equilibrium is greater simply because there are fewer firms.
Note that this does not say
whether firms produce more or less in absolute terms in the new equilibrium.]
When the prisoners’ dilemma is repeated infinite number of times, the likelihood of a
cooperative outcome occurring as a Nash equilibrium is greater when the players place no
value on payoffs beyond the current period.